Begin by preheating your oven to 350°F. Take a 9-inch round cake pan and generously grease it with either butter or baking spray to prevent sticking.
In a medium-sized bowl, combine the all-purpose flour, baking powder, and salt. Use a whisk to mix them thoroughly.
In a larger mixing bowl, or the bowl of a stand mixer equipped with a paddle attachment, beat the softened butter on medium speed until it achieves a creamy texture. Gradually add the granulated sugar, continuing to beat until the mixture becomes light and fluffy, approximately 3 minutes.
Incorporate the eggs one at a time, making sure to scrape down the sides of the bowl and beat well after each addition. Add the sour cream and vanilla extract, and blend until fully integrated.
With the mixer set to low speed, slowly add the flour mixture, blending just until it is combined. Gently fold in about three-quarters of the prepared peaches.
Pour the batter into the greased cake pan, spreading it evenly. Arrange the remaining peaches on top of the batter, and if desired, sprinkle with additional sugar for an extra touch of sweetness.
Place the pan in the oven and bake for about 45 minutes, or until a wooden toothpick inserted into the center of the cake comes out clean. Allow the cake to cool in the pan for at least 30 minutes before serving. This peach cake can be stored covered at room temperature for up to 3 days. Enjoy!